Crystal Defects

Ionic crystals: Brief Review Charge neutrality: the total charge in the base must be zero There are no free electrons, ionic crystals are insulators Interatomic bonding is mostly defined by long-range inter-ionic Coulomb interactions ±q2/r and is rather strong (Ecoul ~ 600-1000 kJ/mol ~ 6-10 eV/atom) and has no directionality NaCl Structure fcc with 2 atoms in the base: at (0, 0, 0) and (½, 0, 0) KCl, AgBr, KBr, PbS, MgO, FeO Na+ ions filling octahedral holes in the fcc structure Fluorite Structure fcc with 3 atoms in the base: cations at (0,0,0) and two anions at (¼, ¼, ¼), and (¼, ¾, ¼) CaF2 or ZrO2 F- ions filling tetrahedral holes in the fcc structure

Ionic crystals: Brief Review CsCl Structure simple cubic with two atoms in the base at (0,0,0) and (½, ½, ½) CsCl, TlI, TlCl AlNi, CuZn - intermetallic comp. Zinc Blende structure fcc with two atoms in the base at (0,0,0) and (¼, ¼, ¼) ZnS, CuF, CuCl GaAs, GaP, InP- Semiconductors tetrahedral sites are preferred because of the relative sizes of the positive and negative ions, but not all of them are filled to maintain stoichiometry Spinel Structure named after the mineral spinel (MgAl2O4) Fe3+( Fe2+ Fe3+)O4, Mg2+( Al23+)O4, Fe3+(Cr23+)O4 can contain vacancies as an integral part of the structure to satisfy the charge balance, Fe21,67Vac2,33O32 if all Fe converted to Fe+3

Crystals Defects Crystal Defects Stoichiometric Non-Stoichiometric Cacat Pusat F (Pusat Warna) Schottky Defect Cacat Akibat Pengotor Frenkel Defect Cacat Bilangan Koordinasi Kation Lebih dari satu

Defect in Ionic crystals, Kröger-Vink Notation The concentration α of vacancies to Na+ sites (or the same concentration of Cl- interstitials) creates net charge of -eαN charge in a crystal with N lattice sites → very high energy → Na1-αCl cannot exist Pure ionic crystals must be perfectly stoichiometric The impurities with different valence and electronegativity than the host ions can require additional point defects to charge balance The concentration of vacancies can be much higher than required by thermal equilibrium-electrochemical equilibrium must be maintained. How to incorporate point defects into chemical reaction equations? X – element symbol for an atom, V for vacancy Y – type of the site occupied by X: (i for an interstitial, element symbol for site normally occupied by this element) Z – charge relative to the normal ion charge on the site ′ negative relative charge • positive relative charge x zero relative charge (x is often omitted)

Defect in Ionic crystals, Kröger-Vink Notation

Schottky Defects Cenderung terjadi Jika Kation dan anion ukurannya relatif sama Penurunan Temperatur dengan cepat dapat menyebabkan kemungkinan cacat Schottky lebih besar Cacat Schottky dapat menurunkan masa jenis kristal

Schottky Defects Schottky defect = cation vacancy + anion vacancy in close proximity formation reaction for a Schottky defect in BeO: this reaction satisfies the mass, charge, and side balance electrostatic attraction between cation and anion vacancies → binding energy of the Schottky defect and temperature dependent degree of association Schottky Defect

Frenkel Defects Kation dapat menempati tempat interstisi (Selitan) apabila: perbandingan jari-jari kation-anion 0,225 – 0,414  Interstisi Tetrahedral perbandingan jari-jari kation-anion 0,414 – 0,732  Interstisi Oktahedral

Anion Frenkel Defects in Frouride Example fluorites include CaF2, SrF2, PbF2, ThO2, UO2, ZrO2 Cation Frenkel defects are common because of the typically smaller size of a cation compared to an anion. However, anions in the fluorite structure have a lower electrical charge than the cations and don’t find it as difficult to move nearer each other. The fluorite structure ccp cations with all tetrahedral holes occupied by the anions – thus all octahedral holes are unoccupied.

Stoichiometric Defects in ionic solids Frenkel defect Cation vacancy + cation interstitial Schottky defect Cation vacancy + anion vacancy

Perubahan G dalam kristal akibat adanya kekosongan DG DH G kristal tanpa cacat DG = DH - TDS neq -TDS

G melibatkan dua hal yaitu: Energi Bebas Gibbs G G melibatkan dua hal yaitu: 1. Enthalpy H =E+PV E internal energy P pressure V volume 2. Entropy S =k ln W k Boltzmann constant W number of microstates G = H – T S T Absolute temperature